While implementing Fast Select, you notice that your pivot p satisfies

Raquel is going on a really long trip, and will need many toys to be entertained. Prof. Brito allows her to use two bags, with capacities respectively. Design a Dynamic Programming algorithm for Raquel such that: given an array W and L for toys numbered , where W is the weight of toy i, and L is the liking coefficient for each toy (the higher L, the more she likes toy i), your algorithm outputs the maximum sum of the L values of both bags. For now, Raquel only has 1 of each toy. Example: W=, L=, , your algorithm should return 8=5+3 as a result of placing toy 2 in the second bag, and toy 4 in the first bag. Note that you can fill the second bag with toys 1 and 4, and place toy 3 in the first bag, but the sum of the L values in this case is 2+3+1=6

The DP table below is the output from the Longest Increasing Subsequence (LIS) algorithm from class, which was run on a sequence A.    1 1 1 2 2 3 4 4   Based on this table, answer questions 12-15.

You are furthermore given the values of the entries of the input A (as a set, not a sequence). True or False: it is possible to reconstruct the sequence A.

In class we described a method, known as chain matrix multiplication (CMM), which determines the fastest way to multiply

You are furthermore given the values of the entries of the input A (as a set, not a sequence). True or False: it is possible to reconstruct the sequence A.

In class we described a method, known as chain matrix multiplication (CMM), which determines the fastest way to multiply

Raquel is going on a really long trip, and will need many toys to be entertained. Prof. Brito allows her to use two bags, with capacities respectively. Design a Dynamic Programming algorithm for Raquel such that: given an array W and L for toys numbered , where W is the weight of toy i, and L is the liking coefficient for each toy (the higher L, the more she likes toy i), your algorithm outputs the maximum sum of the L values of both bags. For now, Raquel only has 1 of each toy. Example: W=, L=, , your algorithm should return 8=5+3 as a result of placing toy 2 in the second bag, and toy 4 in the first bag. Note that you can fill the second bag with toys 1 and 4, and place toy 3 in the first bag, but the sum of the L values in this case is 2+3+1=6

Recall the algorithm discussed in lecture to perform fast multiplication of two integers of n bits. It proposes to recursively compute three multiplications of some integers of n/2 bits, and combine the results using linear many operations. Its runtime is

Recall the algorithm discussed in lecture to perform fast multiplication of two integers of n bits. It proposes to recursively compute three multiplications of some integers of n/2 bits, and combine the results using linear many operations. Its runtime is